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In the section of the Boundless Theorem it may be added, that there exists a more general form where one concludes from ${\displaystyle |f(x,u)|\leq C|u|^{r}+g(x)}$, ${\displaystyle c>0}$, ${\displaystyle r>0}$ that the Nemytskii operator ${\displaystyle F}$ is a bounded and continuous map from ${\displaystyle L^{p}}$ to ${\displaystyle L^{\frac {p}{r}}}$.

This may belong to another article; but I have not found a better place yet.

Jjh1993 ( talk) 11:16, 8 November 2014 (UTC) reply